Gradient-index (GRIN) lenses have a refractive index that varies in one or more coordinate directions. Generally, the refractive index varies in a direction transverse to the intended direction of propagation through the lenses. Parabolic or Gaussian distributions are used for the shape of the index profiles. (Note: The term "index" refers to "refractive index" throughout this specification.)
Three-dimensional GRIN lenses (generally in the 1 to 3 millimeter diameter range) can be made by an ion-exchange process in which a silica glass rod doped with thallium or cesium is immersed in a molten potassium salt bath. Potassium ions from the bath replace some of the thallium or cesium ions in the glass rod by diffusion, leaving a distribution of dopant that progressively decreases toward the periphery of the rod. Such ion distributions provide parabolic-like index profiles in the rods.
Smaller three-dimensional GRIN lenses (e.g., 125 micron diameter) can be made from conventional multi-mode fibers that already have graded-index profiles. The conventional fibers are cleaved to a specific lengths for controlling focusing qualities of the resulting lens. A paper entitled "Analysis and Evaluation of Graded-Index Fiber-Lenses" by W. L. Emkey et al. published in the Journal of Lightwave Technology, Vol. LT-5, No. 9, September 1987 discusses the performance of such fiber lenses.
Two-dimensional (planar) GRIN lenses are more difficult to make. In fact, planar waveguides themselves in which the two-dimensional GRIN lenses are formed require a complex sequence of operations starting with a substrate and laying down successive layers of lower refractive-index cladding surrounding a layer of higher refractive-index core. The required refractive-index profiles are produced by controlling the distribution of dopant in the core layer of the waveguide. The dopant, which typically increases the refractive index in proportion to its concentration, is distributed in concentrations matching the desired index profile. Higher concentrations are distributed at the center of the core, and progressively lower concentrations are distributed approaching the surrounding cladding.
U.S. Pat. No. 4,418,980 to Keil et al. describes the manufacture of planar GRIN lenses through diffusion of titanium into a lithium niobate crystal core. During a sputtering or vapor deposition operation, a shadow mask or variable diaphragm is used to control areas of the core exposed to the dopant. Alternatively, the core can be variably doped by ion implantation.
U.S. Pat. No. 5,157,746 to Tobita et al. describes similar methods for forming planar GRIN lenses. A core layer of PMMA contains styrene or other resin material whose refractive index can be varied through photo polymerization. Ultraviolet light irradiates the core layer through one or more relatively movable masks for varying the amount of area exposed to the light. The resulting index of the core areas varies with the exposure time.
All of these methods are very difficult and expensive to carry out to required accuracy. Most require movements of masks or other apparatus that are difficult to time with other processing variables and can lead to contamination of the core. The various deposition techniques also produce irregularities at interfaces between the core and cladding resulting in reduced transmission efficiencies.